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In fast nonlinear model predictive control the sensitivitycomputation is one of the key aspects to reducecomputational burden, in fact specific automated andefficient procedures for that have been developed. Howeverthe number of sensitivity computations required toadequately approximate the nonlinear dynamics is typicallyhigh and fixed a priori. In this paper, we developa sensitivity updating scheme capable of reducing thenumber of sensitivity computations exploiting an onlinecurvature-based measure of nonlinearity of the system.The proposed strategy is applied to the sequentialquadratic programming framework with specific attentionto the Real-Time Iteration implementation. Simulationson the inverted pendulum benchmark show asignificant reduction of the number of the sensitivity updates,hence a reduction of the overall computationaltime.

We propose a non-linear model predictive scheme for planning fuel efficient maneuvers of small spacecrafts that shall rendezvous space debris. The paper addresses the specific issues of potential limited on-board computational capabilities and low-thrust actuators in the chasing spacecraft, and solves them by using a novel MatLab-based toolbox for real-time non-linear model predictive control (MPC) called MATMPC. This tool computes the MPC rendezvous maneuvering solution in a numerically efficient way, and this allows to greatly extend the prediction horizon length. This implies that the overall MPC scheme can compute solutions that account for the long time-scales that usually characterize the low-thrust rendezvous maneuvers. The so-developed controller is then tested in a realistic scenario that includes all the near-Earth environmental disturbances. We thus show, through numerical simulations, that this MPC method can successfully be used to perform a fuel-efficient rendezvous maneuver with an uncontrolled object, plus evaluate performance indexes such as mission duration, fuel consumption, and robustness against sensor and process noises.